Copula Analysis of Risk: A Multivariate Risk Analysis for VaR and CoVaR using Copulas and DCC-GARCH

Paper: arXiv 2505.06950

Authors: Aryan Singh, Paul O Reilly, Daim Sharif, Patrick Haughey, Eoghan McCarthy, Sathvika Thorali Suresh, Aakhil Anvar, Adarsh Sajeev Kumar

Abstract

A multivariate risk analysis for VaR and CVaR using different copula families is performed on historical financial time series fitted with DCC-GARCH models. A theoretical background is provided alongside a comparison of goodness-of-fit across different copula families to estimate the validity and effectiveness of approaches discussed.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents dense mathematical theory including copulas, DCC-GARCH, and probability transforms, while also detailing a structured empirical methodology with backtesting and goodness-of-fit comparisons.

Research Flowchart

  flowchart TD
  Start["Research Goal<br>Multivariate Risk Analysis<br>for VaR & CoVaR"] --> InputData["Input: Historical<br>Financial Time Series"]
  InputData --> DCCGARCH["DCC-GARCH<br>Model Fitting<br>(Volatility & Correlation)"]
  DCCGARCH --> Residuals["Output:<br>Standardized Residuals"]
  Residuals --> CopulaFit["Copula Fitting<br>(Gaussian, Student-t, etc.)"]
  CopulaFit --> Analysis["Analysis:<br>Risk Metrics Calculation<br>VaR & CoVaR Estimation"]
  Analysis --> Comparison["Goodness-of-Fit<br>Comparison<br>Across Copula Families"]
  Comparison --> Findings["Key Findings:<br>Optimal Copula Selection<br>& Risk Model Validity"]